EP Patent No. 1 422 436 discloses a balance spring whose core is made of single crystal silicon, which is coated with a silicon dioxide coating so as to thermally compensate said balance spring. It also minimises variation in the thermoelastic coefficient as a function of temperature. However, the document only discloses a coating of equal thickness, which may be difficult to adapt it to a balance in order to obtain a resonator with minimum variation of rate.